I cant post to the thread because of my newbie status.

There's a large transaction which hasnt been mined because it depends on some unconfirmed transactions that had no transaction fee. Presumably, they were trying to transfer the BTC from the cold storage to a more secure account, so they want it to happen quickly.

Could they resubmit another transaction? A duplicate of the large one except for the unconfirmed dependency. This would presumably go through fast. It would be a double booking, but they wouldn't care since they are doing it. When the miners get round to it, they will reject the old original transaction.